The present invention relates to seismic reflection surveying and more particularly, relates to the processing and displaying of seismic reflection data to emphasize information in seismic signals reflected from contrasts or differences in elastic constants or densities in the subsurface of the earth accompanied by the presence of potential hydrocarbon reservoirs.
The methods of the present invention which are described herein are generally discussed in terms of compressional-wave (P) seismic data acquisition and processing, which is the most common form of seismic data used in exploration seismology. However, it should be understood that these methods may also be employed for information derived from shear-wave seismic data.
Conventional land or marine seismic acquisition techniques involve the use of an appropriate source to generate seismic energy and a set of receivers, spread out along or near the surface of the earth on land or at or near the water surface or water bottom in a water covered area, to detect any reflected seismic signals due to seismic energy striking subsurface geologic boundaries. These signals are recorded as a function of time and subsequent processing of these time varying signals, i.e. seismic "traces" or seismic data, is designed to reconstruct an appropriate image of the geologic boundaries of the subsurface and to obtain information about the subsurface materials. This conventional process has a seismic wave, from a source of seismic energy, travelling down into the earth, reflecting from a particular geologic interface (i.e. a change or contrast in elastic constants and/or densities), and returning to the surface, where it may be detected by an appropriate receiver.
If the seismic-wave velocity is known as a function of depth and lateral position, and if the position and dip of a planar geologic interface are known, the time for the wave to travel down to that particular reflecting interface and reflect back to the surface can be computed for any source and receiver locations. This two-way travel time is usually described by a function t(X,Z), where Z is the depth to the reflecting interface (contrast in elastic constants or density) and X is the horizontal distance (offset) between source and receiver.
If the elastic constants and densities of the materials above and below a planar reflecting interface are known, then the reflection coefficient for that interface may be computed. This reflection coefficient is the ratio of reflected amplitude to incident amplitude and will depend on the angle of incidence at the reflecting interface. The angle of incidence, .THETA., is the angle between the ray normal to the incident downgoing wavefront and a line normal to the interface; as is well known, the incident( and reflected rays will be in a plane normal to the interface. This angle of incidence increases with increasing offset X. The reflection coefficient for a compressional wave from a particular interface will be designated by the function R.sub.P (.THETA.), where the angle .THETA. may be related to the offset distance X and depth of reflector Z if the compressional-wave velocity at all points in the earth is known; this velocity information, or a reasonable approximation thereto, is referred to as a "velocity model". For a given reflector, the reflection angle, .THETA., and offset, X, are geometrically related, so any discussions herein in terms of dependence upon offset (offset dependence) is equivalent to dependence upon reflection angle (angular dependence). The angular (or offset) dependence of reflection amplitude may be computed exactly for a point source and plane reflector, however in most practical cases it may be approximated adequately by plane-wave reflection coefficients (reflection coefficients for an incident plane wave) which are easily calculated using expressions derived from the results of Zoeppritz (see for example, Young, G. B. and Braile, L. W., Bull Seismol. Soc. Am., Vol. 66, 1976, pp. 1881-1885). For a compressional-wave reflection from a planar interface between two media having a small contrast (i.e., with the medium containing the incident and reflected waves having a compressional velocity V.sub.P, a shear velocity V.sub.S ' and a density .rho., and the other medium having a compressional velocity of V.sub.P +dV.sub.P, a shear velocity VS+dV.sub.S ' and a density .rho.+d.rho., and where dV.sub.P /V.sub.P, dV.sub.S /V.sub.S, and d.rho./.rho. are small compared to one), the offset (or reflection angle) dependence of reflection amplitude may be described for angles of incidence less than the critical angle by an expansion of the form, EQU R.sub.P (.THETA.)=R.sub.P (O+) Ksin.sup.2 (.THETA.)+Lsin.sup.4 (.THETA.)+(1)
For the discussion herein, the angles of incidence are limited to angles such that the terms of the order of sin.sup.4 (.THETA.) and higher are negligible.
In Equation (1), R.sub.P (0) is the normal incidence (.THETA.=0) reflection coefficient; R.sub.P (0) depends only on the densities and compressional velocities of the two media. K is a constant, which also depends on the elastic properties and densities of the media. The relationship of K to the elastic properties and densities may be expressed in a number of ways. One particularly simple expression which relates K to the contrasts in shear velocities, compressional velocities, and densities is EQU K=R.sub..alpha. -4(V.sub.S /V.sub.P).sup.2 (2R.sub..beta. +R.sub.P ),(2)
where EQU R.sub..alpha. =dV.sub.P /(2V.sub.P +dV.sub.P), (2a) EQU R.sub..beta. =dV.sub.S /2V.sub.S +dV.sub.S), and (2b) EQU R.sub..rho. =d.sub..rho. /(2p+dp). (2c)
Also, in terms of these same coefficients, the normal incidence or zero offset reflection coefficients are given exactly by, ##EQU1## For sufficiently small values of R.sub..alpha., R.sub..beta., and R.sub..rho., equations 2d and 2e may be approximated as, EQU R.sub.P (0)=R.sub..alpha. +R.sub..rho., and (2f) EQU R.sub.S (0)=R.sub..beta. +R.sub..rho.. (2g)
Thus, measurement or the normal incidence compressional-wave reflection coefficient, R.sub.P (0), gives information about the densities and compressional velocities, while measurement of the offset dependence constant K can provide information about the densities and shear velocities of the media.
Although the formulas given above are for small contrasts in the elastic properties and densities above and below the planar interface more general theoretical relations may be used. Similar relationships (to equation 1) are well known for the offset dependence of shear-wave reflection coefficients, although the particular form for such shear-wave equations especially those that are analogous to equations 2-2g is quite different. Analogous relations are also well known for mode-converted reflections in which the incident P (or S) wave produces a reflected S (or P) wave. Moreover, the P and S velocities and impedances (impedance is the product of the appropriate velocity and density) may be described as functions of the densities and elastic constants of the materials involved.
There are a number of geologic questions important to exploration for hydrocarbon reservoirs which can be answered by acquiring a knowledge of both the compressional- and shear-wave properties (hereinafter referred to as compressional properties and shear properties) of the subsurface materials. For instance, these materials are generally porous with various fluids filling the pore space. The velocity of a compressional seismic wave in such media depends strongly on the rock matrix properties as well as those of the pore fluid. On the other hand, velocities for shear-wave seismic waves depend strongly on the rock matrix but only slightly on the pore fluid. Thus, detailed study of the properties of the media with both compressional and shear waves provides an opportunity to characterize any changes in seismic response as being due to changes in fluid content (e.g. from brine to oil, or oil to gas) or changes in the rock matrix (e.g. from sandstone to shale or a change in porosity). The ratio of V.sub.P to V.sub.S is often a useful diagnostic feature of such changes. It should be noted that, even without lateral variation, in many cases the recognition of fluid content or rock type may be possible with an accurate knowledge of the compressional and shear properties at a single location. Distinguishing between fluid effects and lithology effects, and detecting different porosity and lithology types are of vital seismic exploration interest and the desire to make such distinctions has engendered significant effort in the measurement and interpretation of shear properties in addition to the information concerning compressional properties traditionally inferred from conventional compressional reflection prospecting.
It is generally the objective of seismic exploration to generate seismic energy, make measurements of the reflection amplitude of this energy at various offsets and for various times, and then, by employing various processing steps on such seismic data, to deduce the geometry as well as some of the elastic properties and densities of the materials of the earth through which the seismic energy has propagated and from which it has been reflected.
Conventional processing of compressional-wave data uses data collected with many sources and many receivers and then sorts the traces according to the "midpoint" between the source and receiver, as illustrated in FIG. 1A. Traces associated with a common midpoint (CMP) are gathered, and used to characterize the subsurface properties below that surface gather point. For example, in FIG. 1A, S.sub.1 and R.sub.1 are the source and receiver pair for the first trace and have a midpoint at the surface point 0. Figure lB depicts the corresponding hyperbolic moveout of such data (where the numbers used correspond to the subscripts used in FIG. 1A) and FIG. 1C depicts the corresponding variation of reflection coefficient with offset for such a case.
The original basis for CMP processing is the fact that each trace in a gather images (or consists of reflections from) approximately the same subsurface points, and, when properly adjusted for differing path lengths, the set of corrected traces may be "stacked" or averaged to give an enhanced picture of the reflection response of the earth below that CMP surface location by emphasizing true primary reflections and discriminating against multiple reflections and other undesirable noise. It is usually assumed that the resulting "stacked" trace represents the normal incidence (zero-offset) response of the earth. While this procedure has been very effective in improving signal-to-noise ratios for seismic data in many areas, it ignores the fact that reflection amplitudes vary as a function of offset and that the stacked trace is not equivalent to a normal incidence trace.
The data is then conventionally displayed as a seismic "section" consisting of the stacked traces arranged side by side in a CMP sequence along the seismic survey line. This display represents a cross-sectional slice of the earth. A set of amplitudes which are recognizably associated on some adjacent traces in a seismic section is called an "event", and is usually assumed to represent seismic reflections from different locations on the same geologic stratum in the subsurface. Many properties of subsurface geologic stratum may be inferred from examination of seismic events and their lateral and vertical variations.
It is sometimes useful to describe events (or other portions of the data) in terms of "attributes". An "attribute" is used herein to mean the result of a specific mathematical operation performed on a portion of the data. For example, seismic data may be processed so that positive amplitudes correspond to strata which have higher impedances than underlying or overlying strata, while negative amplitudes correspond to lower impedance strata. For this example, an event duration attribute may be defined to be the time interval on each trace during which the event's amplitude does not change sign; this attribute is useful because it relates to the thickness of the geologic stratum, although it also depends on the velocity of sound in the stratum and on the bandwidth of the seismic data. Generally attributes are influenced by seismic processing, but their usefulness comes from their dependance on specific properties of the subsurface material.
Methods have been described for measuring and interpreting the variation with offset of the reflection amplitude from a given subsurface interface. Techniques which are tau example in U.S. Pat. Nos. 4,562,558 to Ostrander, 4,573,148 to Herkenhoff et al, 4,570,246 to Herkenhoff et al, 4,316,267 to Ostrander, 4,316,268 to Ostrander, and 4,534,019 et al explicitly describe methods for measuring and interpreting amplitude variation with offset.
As noted above, much attention has been directed to how to interpret amplitude versus offset (AVO) attributes. Some studies have been purely empirical, (Chiburis, E. F., 1987 SEG Expanded Abstracts, Paper S 10.1) measuring the amplitude variation with offset of a particular target event in a particular geographical area, correlating the results to the fluid content of the corresponding stratum found in existing wells in the area, and then predicting the best location for drilling future wells based upon this correlation. This technique is effective, but rules of thumb developed in one area are likely to be less effective elsewhere. In particular, amplitudes rising with offset are not necessary or sufficient to indicate gas or oil sands in the Gulf of Mexico.
Smith and Gidlow (Smith, G. C. and Gidlow, P. M., Geophysical Prospecting, Vol. 35 (1987), pp 993-1014) describe an AVO attribute called the "fluid factor". They estimate V.sub.P and V.sub.S contrasts from AVO, which requires assuming functional forms for .rho.(V.sub.P) and V.sub.P (V.sub.S). These assumed relations are intended to characterize brine-saturated elastic rocks, and are derived from well control or from laboratory data, such as that from Castagna et al (Castagna, J. P., Batzle, M. L. and Eastwood, R. C., Geophysics, Vol. 50 (1985) pp 571-581). The fluid factor is the difference between the V.sub.P contrast estimated from AVO for each seismic event and the one predicted from the assumed V.sub.P (V.sub.S) relation. Smith and Gidlow need to adjust the V.sub.P (V.sub.S) relation in order to "obtain a good result", citing reflection-independent AVO contaminants discussed later herein. Thus, they require some prior knowledge of the relationship between the variables (.rho., V.sub.P, and V.sub.S) and are unable to determine this relationship from the seismic data alone.
These and other limitations and disadvantages of the prior art are overcome by the present invention, however, and improved methods are provided for processing seismic data and displaying information obtained therefrom in a manner to highlight potential hydrocarbon bearing strata.